Acoustic transducers with directional characteristics are useful in many applications. In particular, unidirectional microphones with their relatively large directivity factors for their small size are widely used. Most of these microphones are of the first order gradient type which exhibit, depending on the construction details, directional characteristics described by (a+cos .theta.), where a is a constant (o.ltoreq.a.ltoreq.1) and .theta. is the angle relative to the rotational axis of symmetry. Directivity factors ranging up to four can be obtained with such systems.
The directivity may be improved by utilizing second order gradient microphones. These microphones have a directional pattern given by (a+cos .theta.) (b+cos .theta.) where .vertline.a.vertline..ltoreq..vertline. and .vertline.b.vertline..ltoreq.1 and yield maximum directivity factors of nine. Wide utilization of such microphones was impeded by the more complicated design and the poor signal to noise ratio when compared with the first order designs.
One of the more recent versions of second order gradient microphones is disclosed in U.S. Pat. No. 4,742,548 issued May 3, 1988, for the invention of one of us, James E. West and Gerhard Martin Sessler. While this version represented an advance with respect to prior designs, the relative positioning and sensitivity of the two first-order directional elements employed therein can become overly demanding wherever two or more second-order gradient microphones are to be "matched" or used together, as in an array of such microphones.
Therefore, it is desirable to have an even simpler way to implement a second order gradient microphone and arrays thereof.